Divide the following complex numbers: $\dfrac{4(\cos(\frac{3}{2}\pi) + i \sin(\frac{3}{2}\pi))}{\cos(\pi) + i \sin(\pi)}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $4(\cos(\frac{3}{2}\pi) + i \sin(\frac{3}{2}\pi))$ ) has angle $\frac{3}{2}\pi$ and radius 4. The second number ( $\cos(\pi) + i \sin(\pi)$ ) has angle $1\pi$ and radius 1. The radius of the result will be $\frac{4}{1}$ , which is 4. The angle of the result is $\frac{3}{2}\pi - 1\pi = \frac{1}{2}\pi$ The radius of the result is $4$ and the angle of the result is $\frac{1}{2}\pi$.